论文标题
在三方异质系统中绝对最大的纠缠状态
Absolutely maximally entangled states in tripartite heterogeneous systems
论文作者
论文摘要
绝对最大的纠缠（AME）状态通常在同质系统中定义。但是，量子系统在实际设置中更有可能是异质的。在这项工作中，我们注意三方异质系统中AME州的构建。我们首先介绍了不可约AME状态的概念，这是构建具有较高局部维度的AME状态的基本要素。然后，我们研究了三方异质系统的本地尺寸为$ l，m，n $，$ 3 \ leq l <m <n \ n \ leq m+l-1 $。我们显示了这种异质系统中AME状态的存在与称为Magic Solution Array的阵列有关。我们进一步确定了AME状态在哪种异质系统不可还原。此外，我们提出了一种使用两个现有AME状态来构建更多各方的$ K $统一状态的方法。我们还建立了异质AME状态和多重率矩阵之间的连接，并指示量子转向中的应用。
Absolutely maximally entangled (AME) states are typically defined in homogeneous systems. However, the quantum system is more likely to be heterogeneous in a practical setup. In this work we pay attention to the construction of AME states in tripartite heterogeneous systems. We first introduce the concept of irreducible AME states as the basic elements to construct AME states with high local dimensions. Then we investigate the tripartite heterogeneous systems whose local dimensions are $l,m,n$, with $3\leq l<m<n\leq m+l-1$. We show the existence of AME states in such heterogeneous systems is related to a kind of arrays called magic solution array. We further identify the AME states in which kinds of heterogeneous systems are irreducible. In addition, we propose a method to construct $k$-uniform states of more parties using two existing AME states. We also build the connection between heterogeneous AME states and multi-isometry matrices, and indicate an application in quantum steering.
